English

Occupation densities for certain processes related to fractional Brownian motion

Probability 2008-01-23 v1

Abstract

In this paper we establish the existence of a square integrable occupation density for two classes of stochastic processes. First we consider a Gaussian process with an absolutely continuous random drift, and secondly we handle the case of a (Skorohod) integral with respect to the fractional Brownian motion with Hurst parameter H>12H>\frac 12. The proof of these results uses a general criterion for the existence of a square integrable local time, which is based on the techniques of Malliavin calculus.

Keywords

Cite

@article{arxiv.0801.3314,
  title  = {Occupation densities for certain processes related to fractional Brownian motion},
  author = {Khalifa Es-Sebaiy and David Nualart and Youssef Ouknine and Ciprian Tudor},
  journal= {arXiv preprint arXiv:0801.3314},
  year   = {2008}
}